I'd hardly call it explicitly a Muslim custom - it's common practice throughout south Asia; many Hindus and Buddhists do that as well. It's more of a result of the (historically) extreme poverty in the region, coupled with the arid climate which means that there's often a lack of plant products which are often used in areas of similar poverty but with wetter climates.
However, the fact that the left hand is often used for "personal hygiene" means that various cultural practices have become established - such as never offering food with one's left hand, etc. Again, this is not so much a religious custom so much as it is a regional custom, and is practiced by Hindus and Buddhists as well ... though because of Islam's place of origin the custom is often adopted into the religion and brought along with Islam to places where the orignal reason for the custom is no longer relevant. Hinduism for example does not seek converts so the issue never comes up outside its place of origin.
Bruce
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Interesting comments. I would say then that the islamic custom of cutting off a hand for various offenses would then take on a greater significance than just the loss of that person's specific abilities relative to that one hand. Loss of either hand would force that person to perform hygiene activities with the same hand they handle food with, not to mention the koran (is that desecration?).
Actually in Hinduism it's not so much just the hand, it's the hand washing the butt WITH WATER. And then, according to strict custom, bathing the entire body.